We proposed a prescription to calculate the superconformal index
of \({\cal N}=4\)  \(U(N)\)  SYM
up to an arbitrary order of the \(q\) -expansion
based on the idea of [1]} and
the prescription for the Schur index in [2]}.
We fixed the selection rule for poles associated with hypermultiplets
and \(U(1)_{\rm loop}\)  fugacity \(a^{\prime }_{\rm loop}\) 
so that the poles
at \(u_I\rightarrow 1\)  cancel, and confirmed that the index obtained with the
prescription agrees with the correct one as far as
we have checked numerically.
